\(-\frac{1}{5}\)
\(-\frac{1}{4}\)
\(-\frac{1}{3}\)
\(-\frac{1}{2}\)
Correct answer is B
Sr = \(\frac{a}{1 - r}\)
\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)
\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)
\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)
cross multiply...
-1(8 - 8r) = -10
-8 + 8r = -10
8r = -2
r = -1/4
The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.
24
23
-24
-25
Correct answer is D
n2 - 6n - 4
For the 3rd term,
32 - 6(3) - 4
9 - 18 -4 = -13
For the 4th term,
42 - 6(4) - 4
16 - 24 - 4 = -12
Sum of both terms
-13 - 12 = -25
Find the range of values of m which satisfy (m - 3)(m - 4) < 0
2 < m < 5
-3 < m < 4
3 < m < 4
-4 < m < 3
Correct answer is C
(m - 3)(m - 4) < 0
(m - 3) < 0 ; (m - 4) < 0
m < 3 ; m < 4
3 < m < 4
The value of y for which \(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\) is
\(y > \frac{2}{3}\)
\(y < \frac{2}{3}\)
\(y > -\frac{2}{3}\)
\(y < -\frac{2}{3}\)
Correct answer is C
\(\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}\)
Collect like terms
\(\frac{y}{5} - \frac{y}{2} < \frac{2}{5} - \frac{1}{5}\)
\(\frac{2y - 5y}{10} < \frac{2 - 1}{5}\)
\(\frac{-3y}{10} < \frac{1}{5}\)
\(y > \frac{-2}{3}\)
U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3
24
27
32
36
Correct answer is A
U \(\propto \frac{1}{V^3}\)
U = \(\frac{k}{V^3}\)
k = UV\(^3\)
k = 81 x 2\(^3\) = 81 x 8
When V = 3,
U = \(\frac{k}{V^3}\)
U = \(\frac{81 \times 8}{3^3}\)
U = \(\frac{81 \times 8}{27}\) = 24